Question

The volume and the curved surface area of a cylinder are $1650c{m}^3$ and $660c{m}^2$ respectively. Find the radius and height of the cylinder.

Answer 1

Volume of cylinder = $1650c{m}^3$
and curved surface area = $660c{m}^2$
Let r be the radius and h be the height of the cylinder, then
$\pi r^{2}h=1650$ ...(i)
and $2\pi rh=660$ ...(ii)
Dividing,
$\frac{\pi r^{2}h}{2\pi rh}=\frac{1650}{660}\Rightarrow \frac{r}{2}=\frac{5}{2}\Rightarrow 2r=10\Rightarrow r=\frac{10}{2}=5$
Substituting the value of r in (ii),
$2\pi \times 5h=660\Rightarrow \frac{2\times 22}{7}\times 5h=660$
$h=\frac{660\times 7}{2\times 22\times 5}=21$
$\therefore$ Radius= 5cm
and height= 21cm